This document discusses linear arrays and algorithms for common operations on arrays such as traversing, inserting, deleting, and sorting elements. It defines a linear array as a list of homogeneous data elements with a lower and upper bound. Algorithms provided include traversing from the lower to upper bound, inserting an element at a specified position by shifting other elements and incrementing the size, deleting an element by shifting elements and decrementing the size, and sorting an array using bubble sort by making multiple passes to swap adjacent elements in descending order.

1. Arrays

2. Linear Arrays
A linear array is a list of finite number n of homogeneous
data elements.
Length = UB-LB+1
B: largest index
B: smallest index

3. Memory representation
LOC(LA[K]): add of the element LA[K] of the array LA.
LOC(LA[K])=Base(LA)+W(K-LB)

4. Example
AUTO which records the
number of automobiles sold
each year from 1932 to 1984.
Base(Auto)=200
W=4 words per memory cell
Find the add of element which store
The info about sale in year 1965????

5. Algorithm for traversing an
array
(Traversing a Linear Array) Here LA is a linear array
with lower bound LB and upper bound UB. This
algorithm traverses LA applying an operation
PROCESS to each element of LA.
1. [Initialize counter] Set K := LB.
2. Repeat steps 3 and 4 while K <= UB.
3. [Visit element] Apply PROCESS to LA[K].
4. [Increment counter] Set K := K + 1.
[End of Step 2 loop.]
. Exit.

6. Algorithm for inserting an element into an
array
(Inserting into a linear array) INSERT (LA, N, K, ITEM)
Here LA is a linear array with N elements and K is a
positive integer such that K <= N.
This algorithm inserts an element ITEM into the Kth
position in LA.
1. [Initialize counter.] Set J := N.
2. Repeat Steps 3 and 4 while J >= K.
3. [Move Jth element downward.] Set LA[J+1] :=
LA[J].
4. [Decrease counter.] Set J := J – 1.
[End of Step 2 loop.]
5. [Insert element.] Set LA[K] := ITEM.
6. [Reset N.] Set N := N + 1.
7. Exit.

7. Algorithm for deleting an element from an
array
(Deleting from a linear array) DELETE (LA, N, K, ITEM)
Here LA is a linear array with N elements and K is a
positive integer such that K <= N. This algorithm
deletes the Kth element from LA.
1. Set ITEM := LA[K].
2. Repeat for J = K to N - 1.
[Move J + 1st element upward.] Set LA[J] := LA[J + 1].
[End of loop.]
3. [Reset the number N of elements in LA.] Set N := N - 1.
4. Exit.

8. Algorithm for sorting an array (Bubble
sort)
(Bubble sort) BUBBLE (DATA, N)
Here DATA is an array with N elements. This algorithm sorts
the elements in DATA.
1. Repeat Steps 2 and 3 for K = 1 to N – 1.
2. Set PTR := 1. [Initialize pass pointer PTR.]
3. Repeat while PTR <= (N – K): [Executes pass.]
(a) If DATA[PTR] > DATA[PTR + 1], then:
Interchange DATA[PTR] and DATA[PTR
+ 1].
[End of If structure.]
(b) Set PTR := PTR + 1.
[End of inner loop.]
[End of Step 1 outer loop.]
4. Exit.

9. Example (Bubble sort)
32,51,27,85,66,23,13,57

10. Example (Bubble sort)